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%I #14 Nov 08 2017 04:35:11
%S 1,2,6,21,69,181,375,651,1009,1449,1971,2575,3261,4029,4879,5811,6825,
%T 7921,9099,10359,11701,13125,14631,16219,17889,19641,21475,23391,
%U 25389,27469
%N Number of permutations of length n which avoid the patterns 1234, 2143, 3421.
%H D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 (2017), Table 2 No 3.
%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: A(x) = -{x(18x^6+31x^5+22x^4+8x^3+3x^2-x+1)}/(x-1)^3.
%F FOr n >= 5, a(n) = 41n^2 - 339n + 739. - Franklin T. Adams-Watters, Sep 16 2006
%p cn := [1,-2,2,2,8,22,31,18] ;
%p p := add(cn[i]*x^(i-1),i=1..nops(cn)) ;
%p q := (1-x)^3 ;
%p taylor(p/q,x=0,40) ;
%p gfun[seriestolist](%) ; # _R. J. Mathar_, Nov 07 2017
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006
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